I’m still not following. Either the answer is even in every possible world, or it is odd in every possible world. It can’t be legitimate to consider worlds where it is even and worlds where it is odd, as if they both actually existed.
Either the answer is even in every possible world, or it is odd in every possible world. It can’t be legitimate to consider worlds where it is even and worlds where it is odd, as if they both actually existed.
If you don’t know which is the case, considering such possibly impossible possible worlds is a standard tool. When you’re making a decision, all possible decisions except the actual one are actually impossible, but you still have to consider those possibilities, and infer their morally relevant high-level properties, in the course of coming to a decision. See, for example, Controlling Constant Programs.
Your initial read off your calculator tells you with 99% certainty.
Now Omega comes in and asks you to consider the opposite case. It matters how Omega decided what to say to you. If Omega was always going to contradict your calculator, then what Omega says offers no new information. But if Omega essentially had its own calculator, and was always going to tell you the result even if it didn’t contradict yours, then the probabilities become 50%.
True, but I’d like to jump in and say that you can still make a probability estimate with limited information—that’s the whole point of having probabilities, after all. If you had unlimited information it wouldn’t be much of a probability.
I’m still not following. Either the answer is even in every possible world, or it is odd in every possible world. It can’t be legitimate to consider worlds where it is even and worlds where it is odd, as if they both actually existed.
If you don’t know which is the case, considering such possibly impossible possible worlds is a standard tool. When you’re making a decision, all possible decisions except the actual one are actually impossible, but you still have to consider those possibilities, and infer their morally relevant high-level properties, in the course of coming to a decision. See, for example, Controlling Constant Programs.
Which is the case? What do you do if you’re uncertain about which is the case?
Your initial read off your calculator tells you with 99% certainty.
Now Omega comes in and asks you to consider the opposite case. It matters how Omega decided what to say to you. If Omega was always going to contradict your calculator, then what Omega says offers no new information. But if Omega essentially had its own calculator, and was always going to tell you the result even if it didn’t contradict yours, then the probabilities become 50%.
True, but I’d like to jump in and say that you can still make a probability estimate with limited information—that’s the whole point of having probabilities, after all. If you had unlimited information it wouldn’t be much of a probability.